Melting of Three-Sublattice Order in Easy-Axis Antiferromagnets on Triangular and Kagome Lattices

Abstract

When the constituent spins have an energetic preference to lie along an easy-axis, triangular and Kagome lattice antiferromagnets often develop long-range order that distinguishes the three sublattices of the underlying triangular Bravais lattice. In zero magnetic field, this three-sublattice order melts either in a two-step manner, i.e. via an intermediate phase with power-law threesublattice order controlled by a temperature dependent exponent η(T ) ∈ ( )), providing an easy-to-measure thermodynamic signature of two-step melting. I also show that these two melting scenarios can be generically connected via an intervening multicritical point, and obtain numerical estimates of multicritical exponents. between nearestneighbours [13,14] and weak ferromagnetic Ising interactions between further-neighbours. More recently, the magnetic properties of honeycomb networks [15][16][17][18] of magnetic wires (dubbed artificial Kagome-ice) have been analyzed [19][20][21] in terms of a similar Ising model on the Kagome lattice [22]. In both examples, further-neighbour couplings cause the Ising spins to develop ferrimagnetic three-sublattice order at low temperature, i.e., freeze into a pattern which distinguishes the three sublattices of the underlying triangular Bravais lattice and gives rise to a small net moment along the easy axis.Several other easy-axis spin systems on triangular and Kagome lattices exhibit ferrimagnetic three-sublattice order [23-34], or closely related antiferromagnetic (no net easy-axis moment) three-sublattice order [35]. In zero field (B = 0) along the easy-axis, a Ginzburg-Landau theory [36][37][38] for the three-sublattice order parameter predicts that this ordering transition is described by a six-fold anisotropic effective model of ferromagnetically coupled XY spins [39], or, equivalently, by a generalized six-state clock model [40][41][42][43]. Rather unusually, such sixstate clock models have multiple generic possibilities for continuous transitions: Order is lost either via a two-step melting transition, with an intermediate phase characterized by power-law order [39], or via a sequence of two distinct transitions, one of which is in the three-state Potts universality class and the other in the Ising universality class [40,41]. Perhaps motivated by this, the melting of three-sublattice order has been studied in a variety of triangular and Kagome lattice systems for over three decades now. In some examples [12,[23][24][25][26]35], threesublattice order is known to melt in a two-step manner, via a sizeable intermediate phase with power-law threesublattice order controlled by a temperature-dependent exponent η(T ) ∈ ( 1 9 , 1 4 ). In other examples with ferrimagnetic three-sublattice order, this order is lost via a three-state Potts transition, while residual ferromagnetism is lost via an Ising transition [19][20][21].In this Letter, I analyze the melting of three-sublattice order in easy-axis antiferromagnets on triangular and Kagome lattices using a new coarse-grained description that explici...

Generic nearest-neighbor kagome model: XYZ and Dzyaloshinskii-Moriya couplings with comparison to the pyrochlore-lattice case

“…Example of a configuration with crossing stripes, a possible ground-state for the parameters given in Eqs. (98) and (99). Each color corresponds to one of the eight degenerate ground-states of Fig.…”

Cluster algorithms for frustrated two-dimensional Ising antiferromagnets via dual worm constructions

“…1 of Ref. 38). On both lattices, there is a large range of parameters for which this three-sublattice order melts in a two-step manner on heating, [33][34][35][36][37] via an intermediate phase with powerlaw three-sublattice order corresponding to a temperature dependent power-law exponent η ∈ ( 1 9 , 1 4 ).…”

Tuning the two-step melting of magnetic order in a dipolar kagome spin ice by quantum fluctuations

“…Extensive Monte Carlo simulation of the classical Ising model on triangular and kagome lattices with first, second, and third neighbor interactions have clarified how the two-step melting processes merge into a single first order melting transition 37 . It is then natural to examine the impact of quantum fluctuations on these systems 35 with an eye toward the multicritical point 8 .…”

“…It is also important to bear in mind that the effective theory Eq. 4 is not exactly mapped to a generalized six-state clock model 8 . We shall comment more on this point in Sec.…”